The "system" cannot magically give people equal hashrate because people can own more than one piece of hardware. First you said there were no pools, but now you realise you have no way of preventing them from forming.
This sounds very much like a fanciful wishlist rather than a well considered plan of action.
The beauty of it all is they don`t even need a computer or hash rate to give them equal coins via duration, They just need a address, it could even look like a credit card. Then you don`t even need the hash rate, that can be used on solving diseases.
You can prevent overpowered pools, or giving 1000 votes to 1 guy. That is what we are doing right now, instead of everyone getting 1 vote, some guy because he is rich because of the old bullshit system can buy 10000000000 of votes *asics*.
You want decentralization, this is it. You want a legit money supply, this is it. You want to leave our kind with a future, this is it.